The X-rays pass through the fabric, and they ionize a mixture of gases (Xenon, which is easy to ionize, and CO2, which regulates the size of the signal) in a tube with a high-voltage wire. The ionized gas experiences a little "cascade" - sort of the beginning of a spark - as the free electrons rush towards the high-voltage wire, and the result is a signal that can be read out at the end of the wire. Every particle will make a signal as it passes through, but we will look for the enhancement of the signal due to the extra transition-radiation X rays.